A student performs an experiment to determine the Young's modulus of a wire, exactly`2m` long, by Searle's method. In a partcular reading, the student measures the extension in the length of the wire to be `0.8mm with an uncertainty of `+- 0.05mm` at a load of exactly `1.0kg`, the student also measures the diameter of the wire to be `04mm` with an uncertainty of `+-0.01mm`. Take `g=9.8m//s^(2)` (exact). the Young's modulus obtained from the reading is

Options

A. `(2.0 pm 0.3)xx10^(11) Nm^(-2)`
B. `(2.0 pm 0.2)xx10^(11) Nm^(-2)`
C. `(2.0 pm 0.1)xx10^(11) Nm^(-2)`
D. `(2.0 pm 0.05)xx10^(11) Nm^(-2)`

Answer

b

Explanation

We know that `Y=(mg)/(piD^(2)/4)xxL/l` ltbr gt `(Delta Y)/Y=(2 Delta D)/D+(Delta l)/l`
[Since the value of m, g and L are exact] `=2 0.001/0.4+0.05/0.8`
`=2xx0.025+0.0625`
`=0.05+0.0625=0.1125`
`DeltaY=2xx10^(11)xx0.1125=0.225xx10^(11)`
[Since the value of `Y=2xx10^(11)` in all the four options.]